A009537 - OEIS

%I #21 Jan 07 2019 02:16:50

%S 0,1,0,2,-12,51,-300,2120,-16968,152677,-1526760,16794414,-201532980,

%T 2619928663,-36679001268,550185019124,-8802960306000,149650325201865,

%U -2693705853633552,51180411219037658,-1023608224380753180

%N Expansion of sin(x)*cosh(log(1+x)).

%H Robert Israel, <a href="/A009537/b009537.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) ~ n! * (-1)^(n+1) * sin(1) / 2. - _Vaclav Kotesovec_, Jan 23 2015

%F From _Robert Israel_, Jan 07 2019: (Start)

%F E.g.f.: sin(x)*(1+x+1/(1+x))/2.

%F a(2*k) = (-1)^(k+1)*k - (2*k)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).

%F a(2*k+1) = (-1)^k + (2*k+1)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).

%F (End)

%p S:= series(sin(x)*(1+x+1/(1+x))/2,x,51):

%p seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Jan 07 2019

%t With[{nn=20},CoefficientList[Series[Sin[x]*Cosh[Log[1+x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 20 2015 *)

%t CoefficientList[Series[((1 + (1 + x)^2)*Sin[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Prior Mathematica program replaced by _Harvey P. Dale_, Aug 20 2015